SOME PECULIAR PROPERTIES OF THE RELATIVISTIC OSCILLATOR IN THE POST-GALILEAN APPROXIMATION

In the post-Galilean approximation, the Lagrangians are singular on a submanifold of the phase space, A general analysis of these peculiarit ies, which differ by the ones considered by Dirac, is, up to day, lack ing. The analysis of the dynamics of the one-dimensional and two-dimen sional relativistic oscillators of the second tenser rank, is reported . A comparison with the cases of scalar and vector relativistic oscill ators, described by a regular Lagrangian, is accomplished, Some equili brium statistical properties of the relativistic oscillators are also analysed.